Advertisements
Advertisements
Question
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Advertisements
Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
`tan θ = 1/(sqrt(3)) = tan π/6 ...[∵ tan π/6 = 1/(sqrt(3))]`
∴ the required general solution is
θ = nπ + `pi/(6)`, n ∈ Z.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation have solution or not?
cos 2θ = – 1
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
Find the principal solutions of cos 2𝑥 = 1
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The principal solutions of cot x = `sqrt3` are ______.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
Which of the following equations has no solution?
The general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
The general solution of 4sin2 x = 1 is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
The general solution of cot 4x = –1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
